26 found
Order:
Disambiguations:
Leo Harrington [19]Leo A. Harrington [7]
  1. Leo Harrington & Thomas Jech (1976). On Σ1 Well-Orderings of the Universe. Journal of Symbolic Logic 41 (1):167 - 170.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography  
  2.  1
    Leo Harrington & Saharon Shelah (1985). Some Exact Equiconsistency Results in Set Theory. Notre Dame Journal of Formal Logic 26 (2):178-188.
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   17 citations  
  3.  13
    Jeff Paris & Leo Harrington (1977). A Mathematical Incompleteness in Peano Arithmetic. In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co. 90--1133.
    Direct download  
     
    Export citation  
     
    My bibliography   17 citations  
  4.  6
    Victor Harnik & Leo Harrington (1984). Fundamentals of Forking. Annals of Pure and Applied Logic 26 (3):245-286.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   15 citations  
  5.  4
    Leo Harrington (1977). Long Projective Wellorderings. Annals of Mathematical Logic 12 (1):1-24.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   18 citations  
  6.  14
    Leo Harrington (1978). Analytic Determinacy and 0#. [REVIEW] Journal of Symbolic Logic 43 (4):685 - 693.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   16 citations  
  7. S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare (1991). The D.R.E. Degrees Are Not Dense. Annals of Pure and Applied Logic 55 (2):125-151.
    By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   10 citations  
  8.  36
    Leo Harrington & Robert I. Soare (1996). Definability, Automorphisms, and Dynamic Properties of Computably Enumerable Sets. Bulletin of Symbolic Logic 2 (2):199-213.
    We announce and explain recent results on the computably enumerable (c.e.) sets, especially their definability properties (as sets in the spirit of Cantor), their automorphisms (in the spirit of Felix Klein's Erlanger Programm), their dynamic properties, expressed in terms of how quickly elements enter them relative to elements entering other sets, and the Martin Invariance Conjecture on their Turing degrees, i.e., their information content with respect to relative computability (Turing reducibility).
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  9.  13
    Peter A. Cholak & Leo A. Harrington (2002). On the Definability of the Double Jump in the Computably Enumerable Sets. Journal of Mathematical Logic 2 (02):261-296.
  10.  13
    Peter A. Cholak, Rodney Downey & Leo A. Harrington (2008). The Complexity of Orbits of Computably Enumerable Sets. Bulletin of Symbolic Logic 14 (1):69 - 87.
    The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  11. Leo A. Harrington & Alexander S. Kechris (1981). On the Determinacy of Games on Ordinals. Annals of Mathematical Logic 20 (2):109-154.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   8 citations  
  12.  22
    Peter A. Cholak & Leo A. Harrington (2000). Definable Encodings in the Computably Enumerable Sets. Bulletin of Symbolic Logic 6 (2):185-196.
    Direct download (9 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  13.  4
    Leo Harrington & Robert I. Soare (1998). Definable Properties of the Computably Enumerable Sets. Annals of Pure and Applied Logic 94 (1-3):97-125.
    Post in 1944 began studying properties of a computably enumerable set A such as simple, h-simple, and hh-simple, with the intent of finding a property guaranteeing incompleteness of A . From the observations of Post and Myhill , attention focused by the 1950s on properties definable in the inclusion ordering of c.e. subsets of ω, namely E = . In the 1950s and 1960s Tennenbaum, Martin, Yates, Sacks, Lachlan, Shoenfield and others produced a number of elegant results relating ∄-definable properties (...)
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  14.  18
    Peter A. Cholak & Leo A. Harrington (2003). Isomorphisms of Splits of Computably Enumerable Sets. Journal of Symbolic Logic 68 (3):1044-1064.
    We show that if A and $\widehat{A}$ are automorphic via Φ then the structures $S_{R}(A)$ and $S_{R}(\widehat{A})$ are $\Delta_{3}^{0}-isomorphic$ via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.
    Direct download (9 more)  
     
    Export citation  
     
    My bibliography  
  15.  7
    Leo Harrington & Robert I. Soare (1998). Codable Sets and Orbits of Computably Enumerable Sets. Journal of Symbolic Logic 63 (1):1-28.
    A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has (...)
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  16.  24
    Fred G. Abramson & Leo A. Harrington (1978). Models Without Indiscernibles. Journal of Symbolic Logic 43 (3):572-600.
    For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size $\beth_n$ with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting types over T, H(T), is at least $\beth_\omega$ . (Now, using an upper bound previously obtained by Julia Knight H (true arithmetic) is exactly $\beth_\omega$ ). If T ≠ true arithmetic, then $H(T) = \beth_{\omega1}$ . If $\delta \not\rightarrow (\rho)^{ , then any completion of (...)
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  17. Rod Downey & Leo Harrington (1996). There is No Fat Orbit. Annals of Pure and Applied Logic 80 (3):277-289.
    We give a proof of a theorem of Harrington that there is no orbit of the lattice of recursively enumerable sets containing elements of each nonzero recursively enumerable degree. We also establish some degree theoretical extensions.
    Direct download (3 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  18.  1
    Leo Harrington (1974). Recursively Presentable Prime Models. Journal of Symbolic Logic 39 (2):305-309.
    Direct download (7 more)  
     
    Export citation  
     
    My bibliography   3 citations  
  19.  1
    John T. Baldwin & Leo Harrington (1987). Trivial Pursuit: Remarks on the Main Gap. Annals of Pure and Applied Logic 34 (3):209-230.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography   2 citations  
  20.  1
    Alain Louveau, Jack H. Silver, John P. Burgess, L. Harrington, R. Sami, Maurice Boffa, Dirk van Dalen, Kenneth McAlloon, Leo Harrington, Saharon Shelah, D. van Dalen, D. Lascar, T. J. Smiley & Jacques Stern (1987). Counting the Number of Equivalence Classes of Borel and Coanalytic Equivalence Relations.Equivalences Generated by Families of Borel Sets.A Reflection Phenomenon in Descriptive Set Theory.Equivalence Relations, Projective and Beyond.Counting Equivalence Classes for Co-Κ-Souslin Equivalence Relations.On Lusin's Restricted Continuum Problem. [REVIEW] Journal of Symbolic Logic 52 (3):869.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  21.  2
    Leo Harrington & Thomas Jech (1976). On $Sigma_1$ Well-Orderings of the Universe. Journal of Symbolic Logic 41 (1):167-170.
  22.  3
    Solomon Feferman, Jon Barwise & Leo Harrington (1977). Meeting of the Association for Symbolic Logic: Reno, 1976. Journal of Symbolic Logic 42 (1):156-160.
  23.  3
    Leo A. Harrington & Alexander S. Kechris (1975). On Characterizing Spector Classes. Journal of Symbolic Logic 40 (1):19-24.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography  
  24. Gregory Cherlin, Leo Harrington & Alistair H. Lachlan (1985). ℵ< Sub> 0-Categorical, ℵ< Sub> 0-Stable Structures. Annals of Pure and Applied Logic 28 (2):103-135.
     
    Export citation  
     
    My bibliography  
  25. Gregory Cherlin, Alan Dow, Yuri Gurevich, Leo Harrington, Ulrich Kohlenbach, Phokion Kolaitis, Leonid Levin, Michael Makkai, Ralph McKenzie & Don Pigozzi (2004). University of Illinois at Chicago, Chicago, IL, June 1–4, 2003. Bulletin of Symbolic Logic 10 (1).
     
    Export citation  
     
    My bibliography  
  26. Leo Harrington & Thomas Jech (1976). On Σ1 Well-Orderings of the Universe. Journal of Symbolic Logic 41 (1):167-170.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography